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Martha is 12 times older than her sister.she is 3 times younger than her brother.she is also 4 times older than her cousin .find the age of her cousin if

their total age is 78



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Let cousin's age=x yrs
Then Martha's age=4x
Brother's age=4x/3

Sister's age=4x/12 
Thus cousin's age =11.7 yrs

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Question: Martha is 12 times older than her sister. She is 3 times younger than her brother. She is also 4 times older than her cousin. Find the age of her cousin, if their total age is 78.


Solution:  Let Martha's age be x.

Then, her sister's age will be  \frac{x}{12} .
          Her brother's age will be 3x.
          Her cousins' age will be  \frac{x}{4}

Values of x :

Martha age =  x
Sister age =  \frac{x}{12}
Brother age = 3x
Cousin age =  \frac{x}{4}

Condition or Clue: Their total age is 78.

So, the sum of x \frac{x}{12} 3x, and  \frac{x}{4} is 78.


x+ \frac{x}{12}+3x+ \frac{x}{4}=78


x+ \frac{x}{12}+3x+ \frac{x}{4}=78

=>  x+ \frac{x}{12}+ \frac{x}{4}+3x=78

=>   \frac{12x+x+4x+36x}{12}=78

=>   \frac{53x}{12}=78

=>  x= 78*\frac{12}{53}

=>  x= \frac{78*12}{53}

=>  x= \frac{936}{53}

=>  x=17.660377358490566037735849056604

On rounding it up, we get -



So, Martha's age is x=17.70.
Cousin's age is  \frac{x}{4}= 4.425.
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